REVERSED AND NON-REVERSED SPECTRA. 



105 



To take the case of the submerged glass-plate series 5, if e' be the thick- 

 ness of plate and e" of solution, so that e'-\-e" = e, the thickness of trough, 



- 0*'- i+/v')+ -(//-!+#") = 

 e e e 



Thus, 0.5204 of the data of series (3) added to 0.4796 of the data of series 

 (4) should reproduce series (5). The results are given in table 28. 



TABLE 28. 



These differences are nearly constant and due to the orientation of the 

 glass plate with which its effective thickness (assumed 0.293 cm.) will vary. 



55. Conclusion. It appears, therefore, that the expectation of recognizing 

 the equality of refraction of a submerged solid and a solution, at any given 

 wave-length, from the fixity of the fringes in the presence and absence of 

 the solid has not been fulfilled, at least for the mercury-potassic iodide solu- 

 tion. The reason is found in the enormous difference of the dispersions of the 

 solution and ordinary glass. When the ellipses are not displaced, ju // = 

 2(B'B)/\ 2 , and this difference may even approach a unit in the first decimal 

 of fjL. The troughs in which such experiments are to be made must be optically 

 plane parallel, as otherwise an inadmissible error due to thickness of plates 

 is introduced. With such a trough, however, the ease and accuracy with 

 which the dispersion constants may be found, at least for the solution, are 

 noteworthy. 



When the solution is more refracting than the glass, it is curious that the 

 ellipses are not seriously distorted or vague, even when the symmetrically 

 submerged solid is lenticular. Hence the equation just stated is available 

 for a wide variation of form. Furthermore, if A7V is the displacement at 

 the micrometer corresponding to the presence and absence of glass of the 

 thickness e, 



M -y+ i (S-S')= 

 X 2 e 



But as //, B' for the solution are known, p and B for the glass may both be 

 computed from observation at a number of wave-lengths, X, provided \i = 

 A-\-B/\ 2 for glass, which is sufficiently nearly so to the fourth place of decimals. 

 Hence if AN/e++2B'/\' i = x is known, 



B = 



xx 



3 (i/X 2 -i/X' 2 ) 



